The height profile of a sample, such as a semiconductor substrate, flat panel display, or similar substrates, can be used to determine, e.g., surface roughness, surface curvature, or shape and/or step heights associated with features on the surface of the sample. In the semiconductor industry, for example, it is desirable to measure the height of a step on the surface of the substrate at various times during processing. The height profile of a sample can be conventionally measured in many different ways, such as a single point measurement system, e.g., a contact profilometer or atomic force microscope (AFM), or multiple point measurement system, e.g., a differential interferometer.
One source of error in the measurement of the height profile of features on a sample is caused by tilting. Tilting refers to a constant slope imposed onto a measured height profile, as opposed to an arbitrary shape with a non-zero second derivative (which indicates curvature) imposed onto the height profile.
When determining step heights from a measured height profile, tilting of the sample may result in significant step height errors that are related to the slope of the tilted, measured height profile and the lateral distance over which the profile is measured. FIGS. 1, 2A, and 2B show a level step height profile 10, a tilted step height profile 20, and another titled step height profile 30, respectively. As shown in FIG. 1, the height of step 11, which is h0, is calculated as the vertical distance between points 12 and 14 on the level height profile 10. FIG. 2A, on the other hand, shows that the height of step 21, which is actually h0, is significantly different than step height h1, which is calculated as the vertical distance between points 22 and 24 on the tilted step height profile. FIG. 2A overestimates the height of the step, i.e., h0 is less than h1. FIG. 2B shows an alternative choice for measurement locations 32 and 34 that underestimates the height of the step 31, i.e., h0 is greater than h1. For a tilted height profile, increasing the lateral separation between the two points chosen to determine the step height results in an increased over or under estimation of the step height. Thus, as can be seen, it is imperative to level the height profile of a sample prior to calculating step heights from the height profile. Failure to level will result in a significant over or under estimation of the true step height.
All single point measurement techniques are susceptible to tilting errors due to the imperfect alignment of the metrology tool with the sample. For example, a contact profilometer will display tilting errors when a step on a silicon wafer is scanned. This is caused by the lack of orthogonality of the metrology head (the stylus and vertical height measuring system in a profilometer) to the sample. The flatness of the substrate, the thickness variation across the substrate and the flatness of the chuck that holds the wafer can also contribute to tilting errors. An AFM also exhibits tilting errors due to its single measurement point procedure.
A recent trend in semiconductor processing is to hold a 300 mm diameter silicon substrate by the edges instead of contacting the back of the wafer with a flat, vacuum chuck, in an attempt to minimize contamination of the wafer. Gravitational forces can cause over 100 microns of sagging of the wafer from the edge to the center, which results in another source for (variable) tilting of the wafer. Over small distances, e.g., 200μ, sagging appears as a tilt error with the degree of tilting varying from the center to the edge of the wafer. Over large distances, e.g., 1000μ, sagging appears as curvature.
Conventionally, a contact profilometer or an AFM can level a measured height profile by choosing two locations on the measured height profile that are assumed to be at the same height. Typically, the operator must choose the desired two locations. The software then levels the plot based on these chosen locations. Two more locations on the measured height profile are then chosen to calculate the step height. This procedure can also be executed automatically by designating two positions for leveling and two positions for the step height calculation within a recipe before the measurement is made. The software then levels the plot and calculates the step height automatically. The software is also capable of taking an average over a designated segment of the scan for these four values which generally improves the precision of the measurement. Unfortunately, the tilting related error may still be significant if there are no flat regions or flat regions cannot be properly identified on the height profile.
A differential interferometer is capable of generating a height profile in two different types of scans; a referential scan, which does not need to be corrected for tilting, and a differential scan. In general, a laser differential interferometer projects two laser spots onto the sample surface at two points and scans the two spots across the sample to generate a multitude of measurement points. A height difference between the points on the sample surface causes a difference in the path length between the two beams, which results in a phase difference between the two beams. The measured phase difference can be converted into a step height difference between the two spots with knowledge of the laser wavelength. Typically, an entire line scan is made generating the height profile associated with the scanned area. When collecting the raw data, the sample can be translated with respect to the measurement tool or the measurement tool can be translated with respect to the sample.
In a referential scan, one laser spot acts as a reference and is scanned across a flat region of the sample, while the second laser spot traverses the area of interest. The reference spot compensates for any tilting that may occur in any direction relative to the scan direction because both spots are subjected to the same amount of tilting. Thus, step heights can be accurately and precisely determined from the generated height profile in a referential scan without requiring tilt correction. Typically, even if the metrology tool is perfectly orthogonal to the sample surface, there is also a measured non-zero phase shift between the two spots caused by slight path differences of the two beams in the metrology device. Nevertheless, this error is added to every point of a referential scan and does not impact a step height calculation. For most situations, if the sample exhibits curvature, which often occurs for very long scans, e.g., exceeding 1000 microns, on a semiconductor wafer, a referential scan will not correct the curvature.
In a differential scan, the two spots are closely spaced and follow the same path, with one spot slightly ahead of the other spot. For example, the spot size can be 3 microns and the spacing of the two spots can be 4.5 microns center to center. The profile generated from this plot is not the height profile but the first derivative of the height profile, i.e., the slope of the height profile. Unlike the profile produced by a referential scan, the slope of the height profile produced by a differential scan is susceptible to tilting errors even though two spots are employed. For example, in a flat region of a scan, typically non-zero values of the slope of the height profile are measured due to both tilting of the sample with respect to the metrology device as well as the intrinsic phase shift due to the slight difference in path length traversed by both spots.
One known method used to eliminate tilting error in a differential scan is to always start the scan in a region of the sample that is known to be very flat (or identify a region of the scan that is known to be very flat). The measured value of the slope of the height profile of the flat region of the scan is then subtracted from the remainder of the slope of the height profile data. The flat regions of the scan (regions of the scan that have the same values as the initial part of the scan) will then exhibit a value of zero for the slope of the height profile. When this slope of the height profile data is integrated, the height profile is generated without tilting errors.
Unfortunately, if the scan starts in a region of the sample that is not flat or a flat location along the scan is not known, this procedure will not work. Due to limitations associated with the geometries of features on the surface of typical samples, such as semiconductor wafers, it is not always possible to choose a flat region to start a scan or identify a flat region of the scan. This is particularly true when the measurement procedure is automated and it is desirable to execute the measurements without further human intervention.
Accordingly, there remains a need to accurately level a height profile measurement produced by differential scans of a differential interferometer as well as single point metrology systems to eliminate tilting errors.